Question

a number line shows the ages (in years) that people go to two different movies.
movie 1
1 1 0 3 1 1 2 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 0 1 0 0 1
17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
movie 2
0 1 0 0 1 0 2 0 1 0 2 1 1 2 0 0 3 0 1 1 0 1 0 1 1 0 1
24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

The dot plots show the ages, in years, of people watching two movies at a local theater. Find the median age of the people who watched each movie.

The median age of the people who watched Movie 1 is __.
The median age of the people who watched Movie 2 is __.

find the correct answer for both answers

Answer 1

To find the median age for each movie, we need to follow these steps:

1. **List the ages for each movie based on the frequencies provided.**
2. **Count the total number of people for each movie to find the middle value.**
3. **Determine the median value from the ordered list.**

### Movie 1
The age frequencies for Movie 1 are as follows:
- 17 years: 1
- 18 years: 1
- 19 years: 0
- 20 years: 3
- 21 years: 1
- 22 years: 1
- 23 years: 2
- 24 years: 0
- 25 years: 1
- 26 years: 1
- 27 years: 0
- 28 years: 1
- 29 years: 1
- 30 years: 0
- 31 years: 0
- 32 years: 1
- 33 years: 1
- 34 years: 0
- 35 years: 1
- 36 years: 1
- 37 years: 0
- 38 years: 1
- 39 years: 1
- 40 years: 0
- 41 years: 1
- 42 years: 0
- 43 years: 1

To total the counts:
- Total = 1 + 1 + 0 + 3 + 1 + 1 + 2 + 0 + 1 + 1 + 0 + 1 + 1 + 0 + 0 + 1 + 1 + 0 + 1 + 1 + 0 + 1 + 0 + 1 + 0 + 0 + 1 = 28 people.

### Finding the median for Movie 1:
- The median is the average of the 14th and 15th ages (since \(28/2 = 14\)).
- Listing ages:
- 17, 18, 20, 20, 20, 21, 22, 23, 23, 25, 26, 28, 29, 30, 31, 32, 33, 35, 36, 38, 39, 41, 42, 43.

Identifying the 14th and 15th ages:
- The 14th age is 30.
- The 15th age is 31.

Calculating the median:
\[ \text{Median} = \frac{30 + 31}{2} = 30.5. \]

### Movie 2
The age frequencies for Movie 2 are as follows:
- 24 years: 0
- 25 years: 1
- 26 years: 0
- 27 years: 0
- 28 years: 1
- 29 years: 2
- 30 years: 0
- 31 years: 1
- 32 years: 0
- 33 years: 2
- 34 years: 1
- 35 years: 1
- 36 years: 0
- 37 years: 0
- 38 years: 3
- 39 years: 0
- 40 years: 1
- 41 years: 1
- 42 years: 0
- 43 years: 1
- 44 years: 0
- 45 years: 1
- 46 years: 0
- 47 years: 0
- 48 years: 0
- 49 years: 1
- 50 years: 0

Total = 0 + 1 + 0 + 0 + 1 + 2 + 0 + 1 + 0 + 2 + 1 + 1 + 0 + 0 + 3 + 0 + 1 + 1 + 0 + 1 + 0 + 0 + 0 + 1 = 21 people.

### Finding the median for Movie 2:
- The median is the 11th age (since there are 21 people, \((21+1)/2 = 11\)).
- Listing ages:
- 25, 28, 29, 29, 31, 33, 33, 34, 35, 38, 38, 38, 40, 41, 42, 43, 45, 49.

Identifying the 11th age:
- The 11th age is 38.

### Summary of Medians
- The median age of the people who watched Movie 1 is **30.5**.
- The median age of the people who watched Movie 2 is **38**.

Thus:
- The median age of the people who watched Movie 1 is **30.5**.
- The median age of the people who watched Movie 2 is **38**.